ROME, May 24 (Reuters) - Italian Prime Minister-designate Giuseppe Conte began putting together his cabinet team on Thursday, with party leaders pushing for an 81-year eurosceptic economist to be given the pivotal post of economy minister.

Conte, a law professor without political experience, is meeting all the groups in parliament to discuss his plans, and is unlikely to give the head of state his list of ministers before Friday evening, the 5-Star Movement said.

Plucked from obscurity by the anti-establishment party as the right man to head its coalition with the far-right League, Conte was given the mandate to form a government on Wednesday by President Sergio Mattarella.

League leader Matteo Salvini is expected to take over the interior ministry to pursue his promised crackdown on illegal immigration, while 5-Star chief Luigi Di Maio wants the labour ministry to enact his pledge to improve welfare for the poor.

Like the prime minister, neither Salvini nor Di Maio have any experience of government.

However, the economy ministry is proving most problematic - a potential clash looms between the League and Mattarella, who has the final say on ministerial appointments.

Salvini is lobbying for Paolo Savona, who has decades of experience in academia, banking and government but has spooked markets with his eurosceptic views that chime with the League’s.

Di Maio endorsed the choice on Thursday, saying he and Salvini were seeking “the best people to bring change to this country, and Savona is certainly among these.”

Savona has called Italy’s adoption of the European single currency a “historic error” and calls for a “plan B” to be drawn up to let it leave the euro zone with as little damage as possible should this should prove necessary.

Mattarella, who stresses that Italy must meet its European commitments, has let it be known through his aides that he does not want Savona. Yet Salvini shows no sign of backing down, creating a headache for Conte and potentially undermining the delicate equilibrium of the coalition before it even gets going.

Former prime minister Silvio Berlusconi, an ally of Salvini before the election, said on Thursday his Forza Italia party would vote against the new government in parliament, calling its programme “a naive book of dreams”.

Forza Italia’s votes are not necessary for the 5-Star/League coalition to obtain a majority.

The nascent government has the backing of most Italians, with an opinion poll by the Demopolis agency on Wednesday showing 61 percent were in favour and 39 percent against.

Savona’s appointment would probably alarm EU heavyweight Germany, in particular. He warns in his latest book that the Germans are now trying to dominate Europe economically, having failed to achieve the goal militarily in World War II.

“Savona’s positions are radically and suicidally anti-German,” former Italian economy minister Vincenzo Visco said in an interview in the daily Corriere della Sera on Thursday.

Italian markets, which sold off this week on the prospect of an inexperienced, eurosceptic government taking over the euro zone’s third largest economy, recovered on Thursday morning. Italy’s main share index was up 0.4 percent and the gap between the yield on Italian benchmark bonds and their safer German equivalent narrowed to 184 basis points from 190 on Wednesday. (Reporting by Gavin Jones Editing by Mark Heinrich)